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foreach (@aListMembers) {
    #we only care if its longer than what we already have
...
      my $aList = $hLists{$kLists};
      next if ($iCount <= scalar(@$aList));
    }

mylist_12 sublist153  sublist_34 sublist_123 sublist_345 sublist_245
mylist_1  sublist_153  sublist_87  sublist_876  sublist_78
...
mylist_9  sublist_56 

In the above result, sublist_153 is present in 2 lines.